Given cos A = 6 over radical 61 and that angle A is in Quadrant I, find the exact value of csc A in simplest radical form using a rational denominator

Answer 1

cos A = 6 / √61

cos² A = 36 / 61

sin² A = 1 - (36 / 61)

sin² A = 25 / 61

csc² A = 61 / 25

csc A = ±√61 / 5

Answer 2

cos A = 6 * sqrt(61)/61 <--- rationalizes the denominator

adjacent = 6 * sqrt(61), hypotenuse = 61

pythagorean says: opposite = sqrt ( 61^2 - 26*61) = sqrt( 61(61 - 35)) = sqrt( 61 * 26) = sqrt(1586)

sin A = sqrt(1586)/ 61

csc A = 61 / sqrt(1586) = 61 * sqrt(1586)/ 1586 = sqrt(1586)/ 26